Example Card: Solving Multi-Step Inequalities with Simplification
Solve multi-step inequalities requiring distribution and combining like terms in Grade 9 Algebra. Remember to reverse the inequality sign when multiplying or dividing by a negative.
Key Concepts
Before you can solve, you have to simplify. Let's tackle a multi step inequality that needs a bit of unpacking first.
Example Problem : Solve the inequality $ 5(3 x) \ge 10^2$ and graph the solution.
1. Begin with the inequality. $$ 5(3 x) \ge 10^2 $$ 2. Simplify both sides. Use the distributive property on the left side and evaluate the exponent on the right side. $$ 15 + 5x \ge 100 $$ 3. Add $15$ to both sides to isolate the term with the variable. $$ 5x \ge 85 $$ 4. Divide both sides by $5$. Since $5$ is a positive number, the inequality symbol does not change. $$ x \ge 17 $$ 5. To graph the result, place a closed circle on $ 17$ to show that it is a solution. Then, shade the number line to the right of the circle.
Common Questions
What is Example Card: Solving Multi-Step Inequalities with Simplification in Grade 9 Algebra?
Let's tackle a multi-step inequality that needs a bit of unpacking first Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Example Card: Solving Multi-Step Inequalities with Simplification problems step by step?
Example Problem: Solve the inequality and graph the solution Use this method consistently to avoid common errors.
What is a common mistake when studying Example Card: Solving Multi-Step Inequalities with Simplification?
Use the distributive property on the left side and evaluate the exponent on the right side Always check your work by substituting back into the original problem.